Ionizing Radiation Interaction with Matter

Graham87
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Homework Statement
Problem c)
Relevant Equations
Beer Lambert Law
##\phi(x) = \phi(0) e^{-\mu x}##
##T=e^{-\mu x}##
Screenshot 2024-10-30 104110.png


Basically, I don't understand how they got x=L/2 and x=r paths of T_in and T_out. Below is elaboration.

I don't understand the choice of paths for incoming and outgoing photons in the solution for c).
The solution put incoming path to x=L―/2, while outgoing x=r.
As I interpret it, Tin is the transmission factor before scattering, while Tout is the transmission factor after scattering?
The average photon path traveled in the cylinder is L― and we should divide by 2 for the average path L―/2 before scattering?
Why put the outgoing photons as r? So we assume the photons scatter in the center? But then again we assumed the incoming path is L―/2, which is an average that does not considers all traveling to the center.

So the incoming photons are not assumed to have a mutual path towards the center, while all the outgoing photons should be assumed to travel from the center?

Basically, I don't understand how they got x=L/2 and x=r paths of T_in and T_out.


Screenshot 2024-10-30 104059.png
 
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